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\name{NonLinModelling}
\alias{NonLinModelling}
\alias{tentSim}
\alias{henonSim}
\alias{ikedaSim}
\alias{logisticSim}
\alias{lorentzSim}
\alias{roesslerSim}
\title{Chaotic Time Series Modelling}
\description{
A collection and description of functions to
simulate different types of chaotic time series
maps.
\cr
Chaotic Time Series Maps:
\tabular{ll}{
\code{tentSim} \tab Simulates data from the Tent Map, \cr
\code{henonSim} \tab simulates data from the Henon Map, \cr
\code{ikedaSim} \tab simulates data from the Ikeda Map, \cr
\code{logisticSim} \tab simulates data from the Logistic Map, \cr
\code{lorentzSim} \tab simulates data from the Lorentz Map, \cr
\code{roesslerSim} \tab simulates data from the Roessler Map. }
}
\usage{
tentSim(n = 1000, n.skip = 100, parms = c(a = 2), start = runif(1),
doplot = FALSE)
henonSim(n = 1000, n.skip = 100, parms = c(a = 1.4, b = 0.3),
start = runif(2), doplot = FALSE)
ikedaSim(n = 1000, n.skip = 100, parms = c(a = 0.4, b = 6.0, c = 0.9),
start = runif(2), doplot = FALSE)
logisticSim(n = 1000, n.skip = 100, parms = c(r = 4), start = runif(1),
doplot = FALSE)
lorentzSim(times = seq(0, 40, by = 0.01), parms = c(sigma = 16, r = 45.92,
b = 4), start = c(-14, -13, 47), doplot = TRUE, \dots)
roesslerSim(times = seq(0, 100, by = 0.01), parms = c(a = 0.2, b = 0.2, c = 8.0),
start = c(-1.894, -9.920, 0.0250), doplot = TRUE, \dots)
}
\arguments{
\item{doplot}{
a logical flag. Should a plot be displayed?
}
\item{n, n.skip}{
[henonSim][ikedaSim][logisticSim] - \cr
the number of chaotic time series points to be generated and the
number of initial values to be skipped from the series.
}
\item{parms}{
the named parameter vector characterizing the chaotic map.
}
\item{start}{
the vector of start values to initiate the chaotic map.
}
\item{times}{
[lorentzSim][roesslerSim] - \cr
the sequence of time series points at which to generate the map.
}
\item{\dots}{
arguments to be passed.
}
}
\value{
[*Sim] - \cr
All functions return invisible a vector of time series data.
}
\references{
Brock, W.A., Dechert W.D., Sheinkman J.A. (1987);
\emph{A Test of Independence Based on the Correlation
Dimension},
SSRI no. 8702, Department of Economics, University of
Wisconsin, Madison.
Eckmann J.P., Oliffson Kamphorst S., Ruelle D. (1987),
\emph{Recurrence plots of dynamical systems},
Europhys. Letters 4, 973.
Hegger R., Kantz H., Schreiber T. (1999);
\emph{Practical implementation of nonlinear time series
methods: The TISEAN package},
CHAOS 9, 413--435.
Kennel M.B., Brown R., Abarbanel H.D.I. (1992);
\emph{Determining embedding dimension for phase-space
reconstruction using a geometrical construction},
Phys. Rev. A45, 3403.
Rosenstein M.T., Collins J.J., De Luca C.J. (1993);
\emph{A practical method for calculating largest Lyapunov
exponents from small data sets},
Physica D 65, 117.
}
\seealso{
\code{RandomInnovations}.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## logisticSim -
set.seed(4711)
x = logisticSim(n = 100)
plot(x, main = "Logistic Map")
}
\keyword{models}
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